We employ the relativistic Boltzmann equation to extract the inhomogeneous part of the out-of-equilibrium distribution function. Here we choose the Anderson-Witting type collision kernel [1]} with momentum-dependent relaxation-time (MDRTA). The relaxation time is expressed as \(\tau _{R}=\tau _{R}^{0}\tilde{E}_{p}^{\Lambda }\) , here \(\tau _{R}^{0}\)  is momentum independent [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. To ensure the microscopic conservation of energy-momentum and particle four-current, we propose a linearized collision operator [3]}
\({\cal {L}}_{\text{MDRTA}}[\phi ]=&\frac{\left(p\cdot u\right)}{\tau _R}f^{(0)}(1\pm f^{(0)})\bigg [\phi -\frac{\langle \frac{\tilde{E}_p}{\tau _R}\tilde{E}_p^2\rangle \langle \frac{\tilde{E}_p}{\tau _R}\phi \rangle -\langle \frac{\tilde{E}_p}{\tau _R}\tilde{E}_p\rangle \langle \frac{\tilde{E}_p}{\tau _R}\phi \tilde{E}_p\rangle }{\langle \frac{\tilde{E}_p}{\tau _R}\rangle \langle \frac{\tilde{E}_p}{\tau _R}\tilde{E}_p^2\rangle -\langle \frac{\tilde{E}_p}{\tau _R}\tilde{E}_p\rangle ^2}\nonumber \\&-\tilde{E}_p\frac{\langle \frac{\tilde{E}_p}{\tau _R}\tilde{E}_p\rangle \langle \frac{\tilde{E}_p}{\tau _R}\phi \rangle -\langle \frac{\tilde{E}_p}{\tau _R}\rangle \langle \frac{\tilde{E}_p}{\tau _R}\phi \tilde{E}_p\rangle }{\langle \frac{\tilde{E}_p}{\tau _R}\tilde{E}_p\rangle ^2-\langle \frac{\tilde{E}_p}{\tau _R}\rangle \langle \frac{\tilde{E}_p}{\tau _R}\tilde{E}_p^2\rangle }-\tilde{p}_{\langle \nu \rangle }\frac{\langle \frac{\tilde{E}_p}{\tau _R}\phi \tilde{p}^{\langle \nu \rangle }\rangle }{\frac{1}{3}\langle \frac{\tilde{E}_p}{\tau _R}\tilde{p}^{\langle \mu \rangle }\tilde{p}_{\langle \mu \rangle }\rangle }\bigg ]~.\) 
